Abstract
This chapter provides a compact survey of the binary space B n and related concepts, in particular the eXclusive-OR operation x ⊕ y and its generalization to the binary scalar integral ⊕ n i =1 x i and the binary vector integral ⊕ n i =1 x i for vectors x ∈ B n. We present these mathematical foundations in standard computer science nomenclature, but we will refer also to the nomenclature of APL, because the binary vector integral in section 2.3 has its origin in APL ([IVE62], [IVE78], [LAN93], [LOC89], [ZA95]).
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© 1999 Springer-Verlag Berlin Heidelberg
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Zaus, M. (1999). Mathematical Foundations of Parity Logic. In: Crisp and Soft Computing with Hypercubical Calculus. Studies in Fuzziness and Soft Computing, vol 27. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1879-6_2
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DOI: https://doi.org/10.1007/978-3-7908-1879-6_2
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-662-11380-6
Online ISBN: 978-3-7908-1879-6
eBook Packages: Springer Book Archive